About the Schrödinger Equation
The time-independent Schrödinger equation describes the allowed energy states (wavefunctions) of a quantum particle in a potential. In one dimension, it is:
- (ħ² / 2m) (d²ψ/dx²) + V(x)ψ = Eψ
- ψ(x): Wavefunction (probability amplitude)
- V(x): Potential energy as a function of position
- E: Energy of the state
- ħ: Reduced Planck's constant
- m: Mass of the particle (set to 1 for visualization)
This tool lets you explore solutions for different potentials:
- Infinite Square Well: Particle trapped between two walls
- Potential Barrier: Region with higher potential energy
- Harmonic Oscillator: Parabolic potential (like a spring)